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Is $(1,\ 8)$ a solution to this system of inequalities? $\newline$ $x \leq 2$ $\newline$ $y \leq x + 7$ $\newline$ Choices: $\newline$ (A)yes $\newline$ (B)no

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Is (x, y) a solution to the system of linear inequalities?

Full solution

Q. Is

(1,\ 8)

a solution to this system of inequalities?

\newline

x \leq 2

\newline

y \leq x + 7

\newline

Choices:

\newline

(A)yes

\newline

(B)no

Check Point $1, 8$ : Does the point $1, 8$ satisfy the inequality $x \leq 2$ ? $\newline$ Substitute $1$ for $x$ in $x \leq 2$ . $\newline$ $1 \leq 2$ $\newline$ Since $1 \leq 2$ is true, $1, 8$ satisfies the inequality $x \leq 2$ .
Substitute Values: Does the point $(1, 8)$ satisfy the inequality $y \leq x + 7$ ? $\newline$ Substitute $1$ for $x$ and $8$ for $y$ in $y \leq x + 7$ . $\newline$ $8 \leq 1 + 7$ $\newline$ $8 \leq 8$ $\newline$ Since $8 \leq 8$ is true, $(1, 8)$ satisfies the inequality $y \leq x + 7$ .
Verify Solutions: Is $(1, 8)$ a solution to the system of inequalities? $\newline$ Since $(1, 8)$ satisfies both inequalities $x \leq 2$ and $y \leq x + 7$ , it is a solution to the system of inequalities.

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